In The Clone Wars TV series, (Series 3) Episode 10 entitled "Heroes On Both Sides", the Separatist senator Mina Bonteri (and indeed the other senators who are members of the "Confederacy of Independent Systems") is apparently convinced that Dooku is merely a (Confederate/Separatist) senator:
Padme Amidala: "I sense Dooku's dirty hand in all of this."
Mina Bonteri: "He's just the leader of the Senate, he's not the leader of the entire Universe!"
Padme Amidala: [Sighs] "Oh, I forgot. You actually admire the man."
It is likely that many members of the Confederacy of Independent Systems would be greatly disturbed if they knew that a Sith Lord was controlling their operations- the Confederacy provide funding for the Separatists in the war, and not all of their members are entirely sympathetic to their aims.
While some members of the Confederacy did not hold any qualms negotiating and conspiring with the Sith in the past- such as the Trade Federation and the Galactic Banking Clan, these particular organisations also operate in both Senates in order to enact money-making schemes from the conflict.
The people they are extorting within the Confederacy, however, joined due to their want of remaining independent from the Republic senate, which they feel is corrupt. They didn't sign up for support from Sith Lords, thus Darth Tyranus takes up a pseudonym as Count Dooku, so he is indistinguishable from his real motives.
However, if either side listened to each other more, they would perhaps realise that both their leaders were not as honourable as they made out to be. This probably displays the best example of people believing what they're told, as long as it's in line with what they're inclined to believe.